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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
Quantum Representation of Affine Weyl Groups and Associated Quantum Curves
Sanefumi Moriyamaa, Yasuhiko Yamadab a Department of Physics/OCAMI/NITEP, Osaka City University,
Sugimoto, Osaka 558-8585, Japan
b Department of Mathematics, Kobe University, Rokko, Kobe 657-8501, Japan
Аннотация:
We study a quantum (non-commutative) representation of the affine Weyl group mainly of type $E_8^{(1)}$, where the representation is given by birational actions on two variables $x$, $y$ with $q$-commutation relations. Using the tau variables, we also construct quantum “fundamental” polynomials $F(x,y)$ which completely control the Weyl group actions. The geometric properties of the polynomials $F(x,y)$ for the commutative case is lifted distinctively in the quantum case to certain singularity structures as the $q$-difference operators. This property is further utilized as the characterization of the quantum polynomials $F(x,y)$. As an application, the quantum curve associated with topological strings proposed recently by the first named author is rederived by the Weyl group symmetry. The cases of type $D_5^{(1)}$, $E_6^{(1)}$, $E_7^{(1)}$ are also discussed.
Ключевые слова:
affine Weyl group, quantum curve, Painlevé equation.
Поступила: 13 мая 2021 г.; в окончательном варианте 4 августа 2021 г.; опубликована 15 августа 2021 г.
Образец цитирования:
Sanefumi Moriyama, Yasuhiko Yamada, “Quantum Representation of Affine Weyl Groups and Associated Quantum Curves”, SIGMA, 17 (2021), 076, 24 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1758 https://www.mathnet.ru/rus/sigma/v17/p76
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